# include # include int main ( ); int *julia_set ( int w, int h, float xl, float xr, float yb, float yt ); int julia_value ( int w, int h, float xl, float xr, float yb, float yt, int i, int j ); void tga_write ( int w, int h, unsigned char rgb[], char *filename ); /******************************************************************************/ int main ( ) /******************************************************************************/ /* Purpose: MAIN is the main program for JULIA_CPU. Discussion: Consider points (X,Y) in a rectangular domain R = [XL,XR]x[YB,YT]. Let Z be the complex number X+Yi, and let C be some complex constant. Let Z(0) = Z, Z(k+1) = Z(k)^2 + C The Julia set is the set of points Z in R with the property that the sequence of points Z(k) remain within R. To compute a picture of the Julia set, we choose a discrete array of WxH points in R. We carry out up to 200 steps of the iteration for each point Z. If 1000 < |Z| at any time, we assume Z is not in the Julia set. Licensing: This code is distributed under the GNU LGPL license. Modified: 06 March 2017 Parameters: Local, int H, W, the height and width of the region in pixels. Local, int JULIA, will hold W*H 0 and 1 values, indicating which points are in the Julia set. Local, unsigned char *RGB, will hold W*H*3 values between 0 and 255, specifying the pixel color values. Local, float XL, XR, YB, YT, the left and right X limits, the bottom and top Y limits, of the region. */ { int h = 1000; int i; int j; int *julia; int k; unsigned char *rgb; int w = 1000; float xl = - 1.5; float xr = + 1.5; float yb = - 1.5; float yt = + 1.5; printf ( "\n" ); printf ( "JULIA_CPU:\n" ); printf ( " C version.\n" ); printf ( " Plot a version of the Julia set for Z(k+1)=Z(k)^2-0.8+0.156i\n" ); /* Get the julia values. */ julia = julia_set ( w, h, xl, xr, yb, yt ); /* Create an RGB image of the data. */ k = 0; rgb = ( unsigned char * ) malloc ( w * h * 3 * sizeof ( unsigned char ) ); for ( j = 0; j < h; j++ ) { for ( i = 0; i < w; i++ ) { /* TARGA format orders colors B/G/R! */ rgb[k] = 255 * ( 1 - julia[i+j*w] ); rgb[k+1] = 255 * ( 1 - julia[i+j*w] ); rgb[k+2] = 255; k = k + 3; } } /* Write data to TARGA file. */ tga_write ( w, h, rgb, "julia_cpu.tga" ); /* Free memory. */ free ( julia ); free ( rgb ); /* Terminate. */ printf ( "\n" ); printf ( "JULIA_CPU:\n" ); printf ( " Normal end of execution.\n" ); return 0; } /******************************************************************************/ int *julia_set ( int w, int h, float xl, float xr, float yb, float yt ) /******************************************************************************/ /* Purpose: JULIA_SET checks each point in the domain. Licensing: This code is distributed under the GNU LGPL license. Modified: 06 March 2017 Parameters: Input, int W, H, the width and height of the region in pixels. Input, float XL, XR, YB, YT, the left, right, bottom and top limits. Output, int *JULIA_SET[W*H], 1 if the point is in the Julia set, and 0 otherwise. */ { int i; int j; int *julia; julia = ( int * ) malloc ( w * h * sizeof ( int ) ); for ( j = 0; j < h; j++ ) { for ( i = 0; i < w; i++ ) { julia[i+j*w] = julia_value ( w, h, xl, xr, yb, yt, i, j ); } } return julia; } /******************************************************************************/ int julia_value ( int w, int h, float xl, float xr, float yb, float yt, int i, int j ) /******************************************************************************/ /* Purpose: JULIA_VALUE checks one point in the domain. Discussion: The iteration Z(k+1) = Z(k) + C is used, with C=-0.8+0.156i. Licensing: This code is distributed under the GNU LGPL license. Modified: 06 March 2017 Parameters: Input, int W, H, the width and height of the region in pixels. Input, float XL, XR, YB, YT, the left, right, bottom and top limits. Input, int I, J, the indices of the point to be checked. Ouput, int JULIA, is 1 if the point is in the Julia set. */ { float ai; float ar; float ci = 0.156; float cr = -0.8; int k; float t; int value; float x; float y; /* Convert (I,J) indices to (X,Y) coordinates. */ x = ( ( float ) ( w - i - 1 ) * xl + ( float ) ( i ) * xr ) / ( float ) ( w - 1 ); y = ( ( float ) ( h - j - 1 ) * yb + ( float ) ( j ) * yt ) / ( float ) ( h - 1 ); /* Think of (X,Y) as real and imaginary components of a complex number A = x + y*i. */ ar = x; ai = y; /* A -> A * A + C */ value = 1; for ( k = 0; k < 200; k++ ) { t = ar * ar - ai * ai + cr; ai = ar * ai + ai * ar + ci; ar = t; /* if 1000 < ||A||, reject the point. */ if ( 1000 < ar * ar + ai * ai ) { value = 0; return value; } } return value; } /******************************************************************************/ void tga_write ( int w, int h, unsigned char rgb[], char *filename ) /******************************************************************************/ /* Purpose: TGA_WRITE writes a TGA or TARGA graphics file of the data. Licensing: This code is distributed under the GNU LGPL license. Modified: 06 March 2017 Parameters: Input, int W, H, the width and height of the image. Input, unsigned char RGB[W*H*3], the pixel data. Input, char *FILENAME, the name of the file to contain the screenshot. */ { FILE *file_unit; unsigned char header1[12] = { 0,0,2,0,0,0,0,0,0,0,0,0 }; unsigned char header2[6] = { w%256, w/256, h%256, h/256, 24, 0 }; /* Create the file. */ file_unit = fopen ( filename, "wb" ); /* Write the headers. */ fwrite ( header1, sizeof ( unsigned char ), 12, file_unit ); fwrite ( header2, sizeof ( unsigned char ), 6, file_unit ); /* Write the image data. */ fwrite ( rgb, sizeof ( unsigned char ), 3 * w * h, file_unit ); /* Close the file. */ fclose ( file_unit ); printf ( "\n" ); printf ( "TGA_WRITE:\n" ); printf ( " Graphics data saved as '%s'\n", filename ); return; }